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A154698 Generalized Sierpinski-Pascal-4th gasket triangular sequence generated by T(n, m) = (p^(n-m)*q^m + p^m*q^(n-m))*A(n+1, m+1), where A(n, m) = (3*n -3*k +1)A(n-1, k-1) + (3*k-2)A(n-1, k), A(n,1)=A(n,n)=1, p=2 and q=3. 1
2, 5, 5, 13, 96, 13, 35, 1170, 1170, 35, 97, 12948, 39312, 12948, 97, 275, 142170, 986760, 986760, 142170, 275, 793, 1585368, 22077900, 47364480, 22077900, 1585368, 793, 2315, 18009750, 470999340, 1846449000, 1846449000, 470999340, 18009750, 2315 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are: {2, 10, 122, 2410, 65402, 2258410, 94692602, 4670920810, 264961589882, 16990523224810, 1215217470322682, ...}.

LINKS

G. C. Greubel, Rows n = 0..20 of triangle, flattened

A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, Use of combinatorial algebra for diffusion on fractals, Physical Review A, volume 34, Number 3 (1986) p. 2501, (FIG. 3).

FORMULA

Let p = 2 and q = 3. Starting with the difference equation A(n, m) = (3*n - 3*k + 1)*A(n - 1, k - 1) + (3*k - 2)*A(n - 1, k), where A(n, 1) = A(n, n) = 1, then the triangle is generated by T(n, m) = (p^(n-m)*q^m + p^m*q^(n-m))*A(n+1, m+1).

EXAMPLE

Triangle begins as:

    2;

    5,       5;

   13,      96,       13;

   35,    1170,     1170,       35;

   97,   12948,    39312,    12948,       97;

  275,  142170,   986760,   986760,   142170,     275;

  793, 1585368, 22077900, 47364480, 22077900, 1585368, 793;

MATHEMATICA

p=2; q=3; A[n_, 1]:= 1; A[n_, n_]:= 1; A[n_, k_]:= (3*n-3*k+1)*A[n-1, k-1] + (3*k-2)*A[n-1, k]; T[n_, m_] := (p^(n-m)*q^m + p^m*q^(n-m)) *A[n+1, m+1]; Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 08 2019 *)

CROSSREFS

Sequence in context: A305314 A154694 A154696 * A063786 A121304 A002106

Adjacent sequences:  A154695 A154696 A154697 * A154699 A154700 A154701

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jan 14 2009

EXTENSIONS

Edited by G. C. Greubel, May 08 2019

STATUS

approved

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)